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«by Tae-Yong Kim A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the ...»

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MODELING, RENDERING AND ANIMATING

HUMAN HAIR

by

Tae-Yong Kim

A Dissertation Presented to the

FACULTY OF THE GRADUATE SCHOOL

UNIVERSITY OF SOUTHERN CALIFORNIA

In Partial Fulfillment of the

Requirements of the Degree

DOCTOR OF PHILOSOPHY

(COMPUTER SCIENCE) December 2002 Tae-Yong Kim Copyright 2002 Doctoral Committee Form To be replaced with the actual form ii Acknowledgements It was a long journey to complete this thesis. The journey was truly adventurous and challenging.

Sometimes there were exciting findings along the way, while other times I was so depressed and it seemed that I would never finish this journey. I must confess that without my advisor, Ulrich Neumann, I could have never escaped out of it. Whenever frustrations came, he was there to encourage me. Whenever new findings came out, he was there to congratulate. He is also the best listener I have met in my life. He was always the first person to understand my problems and ideas no matter how significant or insignificant they were. Even when it seemed that I had no clues for some problems, he never forced me his ideas, but discussed all the possibilities and better formulated the problem in his words. Often the times, I would find solutions just by talking to him, and it was a truly amazing experience. I deeply thank him for not only being the source of encouragements, but also teaching me how to become a real scholar and how to do research.

I also would like to thank the other members of my thesis committee, Mathieu Desbrun and Jay Kuo. I am glad I could have them on my committee. Their suggestions and comments helped make this thesis complete and thorough. Through their scrutiny, I was able to evaluate and improve the thesis in totally different perspectives. Mathieu helped me understanding fundamental mathematical concepts, which can be priceless for my future research. I also would like to thank Ellis Horowitz and Ram Nevitia for serving as my qual committee. Ellis is an excellent teacher as well as a joyful racketball partner. Jay and Ram also helped me broadening my knowledge for graphics to images and vision in deeper level.

Special thanks go to J.P. Lewis for his countless help. He is a good friend, an excellent researcher, and a source of virtually any help. His comments for my papers and thesis turned invaluable. His admirable knowledge set always makes me wish I could become such a competent s

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Immersive Technologies laboratory. As one of the early members of the lab, I have seen the lab growing into such a wonderful workplace. Dong Jin Cai, Ken Chen, Young Kwan Cho, Joe Demers, Jun Park, Ilmi Yoon were instrumental for me to find ways through the early stage of my study. Clint Chua, Reyes Enciso, Douglas Fidaleo, Junyong Noh, Bolan Jiang, and Jong Weon Lee have been excellent coworkers who helped me in some of the most critical stages. They are great individuals as well as researchers. Without their holistic supports, I could have never handled many critical problems. I also thank Anand Srinivasan for preparing all the lab equipments for me whenever necessary.

I deeply thank my family for their unconditional love and supports. Without them, none of this would have been possible. My parents always had faiths in me, even when I had disbelief in myself. Without their continuous sacrifice, I would have never done what I present here. I appreciate for their patience, love, and encouragement for their youngest son. My brother and sister always connected deep moral supports although they were thousands miles away at times. I would like to dedicate this thesis to my father who sacrificed everything for us. This thesis is not

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Table of Contents Acknowledgements………………………………………………………………………………….ii List of Tables……...………………………………………………………………………………..vii List of Figures……………………………………………………………………………………..viii Abstract…………………………………………………………………………………………….xii

1. Introduction

1.1 Problem Statement

1.2 Related Work

1.2.1 Surface Representation

1.2.2 Static Pose Hair and Texels

1.2.4 Strand Based Model

1.2.5 Key Hair Approach

1.2.6 Discontinuous Cluster Model

1.2.7 Particles, Fluid flow, and Vector field

1.2.8 Hair Modeling from Photographs

1.2.9 Hair Rendering

1.2.10 Hair Animation

1.3 Thesis Overview

2. Properties of Human Hair

2.1 Properties of a Human Hair Fiber

2.2 Perception Based Analysis of Hair Photographs

2.3 Artistic Drawings of Human Hair

2.4 Human Visual System

2.4.1 Contrast Sensitivity Function

2.4.2 Effect of Visual Masking

2.5 Image Based Hair Rendering and Animation

2.6 Conclusion

3. Thin Shell Volume Modeling

3.1 Shape Function





3.1.1 Notation and Terminology

3.1.2 TSV Generation and Volume Warping

3.2 Virtual Hair Combing

3.2.1 Particle Selection (pickup)

3.2.2 Particle Redistribution (s-direction)

3.2.3 Sweeping Effect

3.2.4 Vertical Motion (u-direction)

3.3 Rendering TSV

3.3.1 Probabilistic Shadow Generation

3.3.2 Shading and Antialiasing

3.4 Implementation and Results

3.A Coons Patch

4. Interactive Multiresolution Hair Modeling and Editing

4.1 Overview

4.2 Hair Cluster Representation

4.2.1 Generalized Cylinder

v 4.2.2 Representation of Contour

4.2.3 Auxiliary Functions

4.3 Scalp Surface

4.4 Generation of Hair Strands

4.5 Subdivision

4.5.1 Deciding the Owners of Hair Strands

4.6 Interactive Manipulation

4.6.1 Editing Properties of Hair Clusters

4.6.2 Copy and Paste

4.6.3 Selection Methods

4.6.4 Avoiding Hair-Head Penetration

4.7 Level of Detail and Interactive Rendering

4.8 Results

4.9 Implementation Details

4.10 Conclusion

5. Fundamentals of Hair Image Synthesis

5.1 Aliasing and Sampling Theory

5.2 Volume Rendering Equation for Hair Rendering

5.3 The Phase Function

5.4 Hair Shading Model

5.5 Yet Another Shading Model

5.5.1 Emprical Model

5.5.2 Simulated Model with a Single Layer

5.5.3 Discussion

5.5.4 Recap

5.6 Shadows and Primary Scattering

5.7 Sampling the Radiance

5.8 Other Issues

5.9 Hardware Accelerated Hair Rendering

6. Interactive Hair Rendering

6.1 Overview

6.2 Hair Self-shadows by Opacity Maps

6.2.1 Basic Algorithm

6.2.2 Result and Performance

6.2.3 Discussion

6.2.4 Comparison with Other Methods

6.2.5 Extensions

6.3 Anitialiasing

6.3.1 A Simple Visibility Ordering Algorithm

6.3.2 Discussion

6.4 Conclusion

7. Animation and Future work

7.1 Towards Interactive Hair Animation

7.2 Hair Strand Dynamics

7.2.1 Cantilever Beam and One Dimensional Angular Dynamics

7.2.2 Forward Kinematics

7.2.3 Mass-Spring Simulation

7.3 Collision Detection and Interaction Handling

vi

7.4 Multiresolution Framework for Hair Animation

7.5 Future Work

7.6 Conclusion

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List of Tables 4-1 Time measurements for components of MHM system……………………………65 6-1 Pseudo code for opacity shadow maps algorithm………………………………..106 6-2 Comparison with deep shadow maps…………………………………………….113

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List of Figures 1-1 Schematic diagram of hair design process………………………………………….6 2-1 Cross section of a human hair fiber………………………………………………..18 2-2 Photographs of human hairs at multiple scales……………………………………21 2-3 The contrast sensitivity function…………………………………………………...24 3-1 Overview of hair coming using a thin shell volume model………………………..29 3-2 Cross section of a TSV…………………………………………………………….31 3-3 Generation of a TSV……………………………………………………………….31 3-4 Virtual hair combing……………………………………………………………….33 3-5 Hair density changes during combing……………………………………………..35 3-6 A hair strand is bent along the path of the comb’s tooth…………………………..36 3-7 Vertical motion………………………………………………………………….…36 3-8 A hair design with 4 patches…………………………………………………….…40 3-9 Result of hair combing………………………………………………………….…40 3-10 Animation of TSV…………………………………………………………………41 3-11 The effect of different combing functions…………………………………………42 4-1 An example hair design process…………………………………………………...45 4-2 Graphical view of a multiresolution hair model…………………………………...46 4-3 Creating a generalized cylinder……………………………………………………47 4-4 Effects of different reference frames………………………………………………48 4-5 Definition of a reference frame along the space curve………………………….…49 4-6 Effects of auxiliary terms………………………………………………………….50 4-7 Placing a contour on the scalp……………………………………………………..51

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4-9 Hair strand generation schemes……………………………………………………53 4-10 Scalp space contours can overlap each other………………………………………53 4-11 Guaranteeing the smoothness of a hair strand……………………………………..55 4-12 Self-intersection problem………………………………………………………….55 4-13 Subdivision of contours and tiling of the scalp space…………………………..…56 4-14 Hair strand assignment patterns………………………………………………...….57 4-15 Hair ownership decision algorithm…………………………………………….…..58 4-16 Interactive manipulation of a hair cluster……………………………………….…59 4-17 Temporary and local binding………………………………………………………61 4-18 Copying a braid from one cluster to another………………………………………62 4-19 A braid style resulting from multiple copy/paste operations at multiple scales…...63 4-20 The complexity of a multiresolution hair model…………………………………..63 4-21 Closest point transform of the head mesh…………………………………..……..64 4-22 Avoiding hair-head penetration……………………………………………..……..64 4-23 Effects of shadows and level of detail……………………………………………..66 4-24 Designing a complex hairstyle…………………………………………………….67 4-25 A smooth hairstyle…………………………………………………………………67 4-26 More hairstyles……………………………………………………………………68 4-27 Curly ponytail……………………………………………………………………..69 5-1 Consequences of point sampling in the presence of complex geometry………….75 5-2 A hair strand is assumed to be a straight cylinder…………………………………79 5-3 Hair shading geometry…………………………………………………………….80 5-4 The direction vectors can be expressed by polar coordinates …………………….81 5-5 A cross-section of a semi-transparent cylinder…………………………………….85

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